   SEARCH HOME Math Central Quandaries & Queries  Question from maya, a student: eric bought 3 sweaters and 1 pair of pants. Each sweater cost d dollars and the pants cost 20 dollars. Eric spent a total of 95 dollars. The equation below can be used to determine the cost of each sweater. what is the answer? Maya,

The numbers in this problem are chosen to make the arithmetic easy. As a result you don't need algebra to solve it you can do it in your head. Let's do it that way and then write the solution using algebraic notation.

The pants cost $20 and the total cost was$95 so the three sweaters cost $95 -$20 = $75. Hence, since 3 sweaters cost$75 dollars the cost of each sweater was $25. I am going to change the problem slightly so that the arithmetic isn't quite so easy and then use algebra to solve it. erin went to the store next door and bought 3 sweaters and 1 pair of pants. Each sweater cost d dollars and the pants cost 20 dollars. Erin spent a total of 92.36 dollars. What is the cost of each sweater. The cost for the pants was 20 dollars and each of the three sweaters cost d dollars so the total cost of the sweaters was 3 × d dollars. Thus the total cost was 20 + 3 × d dollars. We know the total cost was 92.36 dollars so 20 + 3 × d = 92.36. This is the equation I am looking for. In the first problem I subtracted 20 dollars from 95 dollars to determine the total cost of the three sweaters. Yo do the same here. Subtract 20 from each side of the equation to get 20 + 3 × d - 20 = 92.36 - 20 or 3 × d = 72.36. In the first problem the total cost of the three sweaters was$75 so it was easy to see that each sweater cost $25 since$75/3 = $25. In the current problem you have 3 × d = 72.36 and if you divide both sides by 3 you get (3 × d)/3 = 72.36/3 or d = 24.12. So each sweater cost$24.12.

Now try the algebraic approach on the first problem.
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.